Finite Group Databasebeta

C16×Dic58 #16821395

order3712
isoclinismisoclinic class of Dic58
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC16×Dic58

Splittings

SylowC29 ⋊ Q8×C16

Subgroups

subgroupG/H
centerC2×C16C2×D29
commutatorC2×C29C22×C16
FrattiniC2×C8C22×D29
FittingC4×C16×C29C2
socle, prime radicalC22×C29C22×C8
cosocleC2×C8×C29C23
hypercenterC4×C16D29
hypocenterC29Q8×C16
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C16 ◁ C4×C16

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 6413);